Homework Help:
Limit of this sequence.

I want to show that this sequence converges to 0, i.e. given any positive real number 'r', I want to show that there exists a natural number k such that xk < r. (The sequence is monotonically decreasing.)

I want to show that this sequence converges to 0, i.e. given any positive real number 'r', I want to show that there exists a natural number k such that xk < r. (The sequence is monotonically decreasing.)

Help please.

Find an upper bound for [1 + 1/2 + 1/3 + ... + 1/n] using an integral to estimate it. That would be a good start.

Isn't it something like the integral test? It was kinda obvious from the diagram.
And lim [x^x] -> 1 as x->0 follows from L'Hopital's rule. (The log of the limit is 0)

Yes, it is l'Hopital, but I don't see what x^x has to do with it. And yes, the integral part is sort of obvious from a lower sum estimate of 1/x. If you don't want to actually spell out the details, that's fine with me.